Factors, multiples and primes: what children learn
Year 5 pupils learn to identify multiples and factors, find all the factor pairs of a number and common factors of two numbers, and use the words prime, prime factor and composite. They should be able to decide whether a number up to 100 is prime and recall the prime numbers up to 19.
The quiz mixes three types of question: 'Which of these is a prime number?', 'Which of these is a factor of 36?' and 'Which of these is a multiple of 7?'. Exactly one of the four choices is correct each time. For the prime questions, the wrong choices are odd numbers that look prime but are not, such as 51, 57 and 91.
This topic covers the Year 5 statutory requirement in the National Curriculum in England (Number – multiplication and division): pupils should be taught to “identify multiples and factors, including finding all factor pairs of a number; establish whether a number up to 100 is prime and recall prime numbers up to 19”. Year 5 pupils are usually aged 9–10.
For families following US standards, the closest Common Core standard is 4.OA.B.4, which is taught in Grade 4.
How to play
Answer 10 questions before the clock runs out. Tap an answer, or press 1 to 4. Each game has 10 multiple-choice questions and a 120-second timer. A wrong answer shows the correct one before moving on. You earn up to three stars depending on your score.
Step by step
- Factors divide exactly. A factor of a number divides into it with no remainder. 6 is a factor of 24 because 24 ÷ 6 = 4.
- Find factors in pairs. Work up from 1: 1 × 24, 2 × 12, 3 × 8, 4 × 6. When the pairs start repeating, you have found them all. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
- Multiples are in the times table. The multiples of 7 are 7, 14, 21, 28 and so on. A number is a multiple of 7 if 7 is one of its factors.
- Test for primes. A prime number has exactly two factors: 1 and itself. To test a number up to 100, check whether 2, 3, 5 or 7 divide it exactly. If none do, it is prime. 1 is not prime, because it has only one factor.
Worked examples
Example 1: Is 91 prime?
Working: 91 is odd, its digits add to 10 so it is not divisible by 3, and it does not end in 0 or 5. But 91 ÷ 7 = 13.
Answer: No, 91 = 7 × 13
Example 2: Which of 5, 7, 8, 9 is a factor of 63?
Working: 63 ÷ 7 = 9 and 63 ÷ 9 = 7, so both 7 and 9 divide 63. The game avoids this by only ever having one correct choice.
Answer: 7 and 9 are both factors
Example 3: What are the common factors of 12 and 18?
Working: Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. The numbers in both lists are the common factors.
Answer: 1, 2, 3 and 6
Common mistakes and how to fix them
- Thinking 1 is a prime number. A prime has exactly two different factors. 1 has only one, so it is neither prime nor composite.
- Thinking all odd numbers are prime. Look at 9, 15, 21, 27, 49 and 91. Test each with 3, 5 and 7.
- Mixing up factors and multiples. Factors are small and fit into the number; multiples are big and come out of it. Factors of 12: 1, 2, 3, 4, 6, 12. Multiples of 12: 12, 24, 36…
Activities to try at home
- Arrange 24 small objects into as many different rectangles as you can. Each rectangle shows a factor pair.
- Find prime numbers on number plates or in dates.
- Play 'factor or multiple?' where one person says two numbers and the other decides which relationship they have.
Ideas for the classroom
- Use the Sieve of Eratosthenes on a 100 square to find all the primes to 100.
- Make factor rainbows by drawing arcs between factor pairs.
- Explore which numbers have an odd number of factors (they are the square numbers).
Printable worksheet
The printable worksheet uses the same question generator as the game, so it practises exactly the same skills. It comes with a separate answer sheet on the second page. Print it, or save it as a PDF from your browser's print menu.
Frequently asked questions
What are the prime numbers up to 19?
2, 3, 5, 7, 11, 13, 17 and 19. Year 5 pupils are expected to recall these.
Is 2 a prime number?
Yes. It is the only even prime number, because every other even number has 2 as a factor.
What is a composite number?
A whole number greater than 1 that is not prime, so it has more than two factors. For example, 12 is composite.
What is the US equivalent?
Common Core 4.OA.B.4 (Grade 4): find all factor pairs for a whole number from 1 to 100, and determine whether it is prime or composite.